A) \[\frac{{{e}^{a}}{{b}^{n}}}{n!}\]
B) \[\frac{{{(b\cdot a)}^{n}}}{n}\]
C) \[\frac{{{e}^{b}}\cdot {{b}^{n}}}{(n-1)!}\]
D) \[\frac{{{a}^{n}}\cdot {{b}^{n-1}}}{n!}\]
Correct Answer: A
Solution :
We know, \[{{e}^{x}}=1+\frac{x}{1!}+\frac{{{x}^{2}}}{2!}+\frac{{{x}^{3}}}{3!}+...\] Put \[x=(a+bx)\] \[\therefore \] \[{{e}^{a+bx}}=1+\frac{a+bx}{1!}+\frac{{{(a+bx)}^{2}}}{2!}\] \[+\frac{{{(a+bx)}^{3}}}{3!}+...\] \[\therefore \] Coefficient of\[{{x}^{n}}\]in\[{{e}^{a+bx}}\] \[={{e}^{a}}\frac{{{(b)}^{n}}}{n!}\]
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